New Progress of Grey System Theory in The New Millennium

Purpose – The purpose of this paper is to summarize the progress in grey system research during 2000- 2015, so as to present some important new concepts, models, methods and a new framework of grey system theory. Design/methodology/approach –The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “Kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of GM(1,1), such as Even Grey Model(EGM), Original Difference Grey Model(ODGM), Even Difference Grey Model(EDGM), Discrete Grey Model(DGM) and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well. Findings –The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper. Practical implications – A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science, and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate. Originality/value –The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section. Keywords Grey systems theory, Operations of grey numbers, Buffer operators, Grey forecasting models, Grey incidence analysis models, Grey cluster evaluation models, Grey decision models, Combined grey models, Grey contro

A greyness reduction framework for prediction of grey heterogeneous data

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Existing operational rules of interval grey numbers do not make full use of possible background information when determining the interval boundaries, and this may result in inconsistent results if applying different logical operations. This paper finds that multiplication and division rules of interval grey numbers do not meet the calculation rule of inverse operators. Direct solution and inverse solution of the same interval grey number object may differ not only in numerical ranges but also in greyness degrees. To improve the accuracy of grey number calculation, new operational rules for multiplication and division of interval grey numbers are proposed. Then the traditional prediction modeling method of grey heterogeneous data is refined and expanded by integrating a greyness reduction preprocessing, which is based on the proposed calculation rules. Application of the expanded heterogeneous interval grey number prediction model to a stock replenishment scheduling problem in emergency rescue scenarios is included to illustrate the new operational rules of grey numbers and their application in prediction algorithm, and the proposed approach is compared with other existing methods to demonstrate its effectiveness